A little thought of before the Big Bang

[Peter Watkins]

Quite how Chronos figured that I view the universe as a giant black hole is difficult to imagine. It is a flight of fancy that exceeds even that of dark energy and expanding space.
With regard to the reversal of gravity at extreme densities, how would that work? Surely, once the reversed gravity caused a degree or so of expansion, density would decrease, gravity would revert and collapse would commence once again, leading to renewed expansion, and so on, an infinitum. All within tiny time cycles I assume. It doesn't sound like a realistic proposal for the bringing into being of our little universe.

 

[Chalnoth]

With regard to the reversal of gravity at extreme densities, how would that work? Surely, once the reversed gravity caused a degree or so of expansion, density would decrease, gravity would revert and collapse would commence once again, leading to renewed expansion, and so on, an infinitum. All within tiny time cycles I assume. It doesn't sound like a realistic proposal for the bringing into being of our little universe.

Well, I really don't know, but here's one scenario under which you might get a sort of bounce:

Imagine, for a moment, that if matter is condensed to extraordinary amounts (as you'd get near the center of a black hole), that it tends to start to transfer its energy into a sort of a scalar field that acts like an inflaton, and you end up with a small region of space that has an exceedingly high energy density spread relatively evenly across said region. If matter tends to approach this configuration at the highest of densities, then it would tend to produce an inflating region of space. Now, because of the geometry, there's no way this inflating region could expand into the surrounding space, but would instead produce new space within its own region, sort of expanding "out the bottom" of the black hole.

This is just a pie-in-the-sky idea, though. I have no idea if the actual bounce ideas are like this, or if it's remotely likely. But it's one on-the-surface plausible way in which you might get a sort of "bounce".

 

[Chalnoth]

By the way, I'd like to add on a little bit of an explanation for my previous reply to Chronos on our universe being a black hole when viewed from the outside:

First, the limit to which we can see with visible light is the surface of last scattering. We know that our universe extends beyond this for quite some ways, but that's okay for this calculation. The idea is pretty simple: let's imagine, just for kicks, that our universe ends just beyond the CMB (this isn't really possible, but it serves as a fair thought experiment). Beyond that, there is nothing but empty space (and dark energy).

In this little thought experiment, that would make our universe a spherically-symmetric universe with a given mass. I compute the average normal/dark matter density of the universe, from the WMAP 5-year best-fit parameters, as being:
\rho_m = 2.49 \times 10^{-24} \mathrm{gm/m^3}

Given this, the total mass of our universe out to the surface of last scattering is:
m = 8.91 \times 10^{56} ~\mathrm{gm}

That's a fairly big number. But what's the Schwarzschild radius for a mass this large? Well:
r_s = \frac{2Gm}{c^2} = 42,900 ~\mathrm{Mpc}

Compare that to the distance to the surface of last scattering:
d_A = 14,279 \mathrm{Mpc}

Now, given the nature of Gauss's Law, it seems to me that this means that if our universe suddenly ends just past the limits of our vision, then the collective gravity of everything in our visible universe makes it so that when viewed from outside, our universe would look like a black hole (since it'd be surrounded by an event horizon with area given by the radius 42,900 Mpc).

But what if we step back a moment, and recognize that our universe doesn't end just beyond the limits of our vision? This is pretty much necessarily the case, as we don't expect an abrupt end to our universe, but instead some sort of tapering off or some such. In that situation, then we have to examine how the Schwarzschild radius r_s scales with increased size.

That's pretty easy to do. Just consider that the Schwarzschild radius r_s is linear with mass, but mass increases as the cube of the radius of the universe. This means that if the universe extends beyond the limits of our vision, then the Schwarzschild radius gets even larger.

Therefore it definitely appears to me that our universe, if it has any boundary, must have an event horizon outside of that boundary, hiding it our region of space-time from communicating with any other: we would look like a black hole to anybody "outside" our universe.